Bayesian propensity scores for high‐dimensional causal inference: A comparison of drug‐eluting to bare‐metal coronary stents

Abstract

High-dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high-dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem.

A comparison of machine learning algorithms and covariate balance measures for propensity score matching and weighting

“…In both cases we observed similar average weights between treated and control groups and in both cases we detect the presence of few outliers. High weights can indicate a positivity violation, though low weights are no guarantee of good overlap (Cole & Hernan, ; Spertus & Normand, ) and ad hoc diagnostics for positivity violations have been suggested (e.g., Peterson et al., 2012). Exploring this issue further goes beyond the scope of this work.…”

“…In both cases we observed similar average weights between treated and control groups and in both cases we detect the presence of few outliers. High weights can indicate a positivity violation, though low weights are no guarantee of good overlap (Cole & Hernan, 2008;Spertus & Normand, 2018) and ad hoc diagnostics for positivity violations have been F I G U R E 6 Ninety-five percent confidence interval (CI) coverage probability of propensity score matching (PSM) and propensity score weighting (PSW) estimators of average treatment effect (ATE) based on logistic regression and different machine learning (ML) techniques by scenario, simulation study 2. Light gray bars for PSM; dark gray bars for PSW suggested (e.g., Peterson et al, 2012).…”

“…In this way, unbiased estimates of the treatment can be obtained relatively easily, for example, by direct comparison of the outcome means across the two groups. However, because of ethical or practical reasons in many situations researchers have to rely on nonexperimental or, following Cochran's definition (), observational data, see for example, the recent application in Spertus and Normand () on the estimation of two treatment alternatives for percutaneous coronary interventions on mortality.…”

“…nonexperimental or, following Cochran's definition (1965), observational data, see for example, the recent application in Spertus and Normand (2018) on the estimation of two treatment alternatives for percutaneous coronary interventions on mortality.…”

Obstructive sleep apnoea, positive airway pressure treatment and postoperative delirium: protocol for a retrospective observational study

“…We will create propensity scores for OSA diagnosis or high STOP-BANG using non-parametric regression. We will use the fitted propensity score and covariates in a flexible regression method based on an ensemble of decision trees (Bayesian Adaptive Regression Trees (BART)46); this two-stage approach has been shown to be valid and robust,47–49 accounting for the uncertainty in the mechanisms of exposure and allowing nonlinear effects, interaction terms and heterogeneity of treatment effects 50–53. As a sensitivity analysis we will compare the average treatment effect on the treated from our primary analysis with propensity score matching based estimates of the same with greedy 1:1 matching 54–56.…”